A216059 Smallest number not in Collatz trajectory starting at n.

2, 3, 6, 3, 3, 7, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Author

Reinhard Zumkeller, Sep 01 2012

Keywords

• nonn

Comments

a(n) <= 7; a(A007283(n)) = 7;

a(n) <> 4; a(n) <> 4; a(n) <> 6 for n > 3;

a(n) = A216022(n) + 1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Collatz Problem
• Wikipedia, Collatz conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006370, A070165.

Programs

Haskell

import Data.List ((\\))
a216059  n = head $ enumFromTo 1 (maximum ts + 1) \\ ts
   where ts = a070165_row n

Mathematica

scoll[n_]:=Sort[NestWhileList[If[EvenQ[#],#/2,3#+1] &,n,#>1 &]]; Join[{2,3},Table[i=1; While[scoll[n][[i]]==i,i++]; i,{n,3,86}]] (* Jayanta Basu, May 27 2013 *)